Approximation Schemes for Planar Graph Problems

Years and Authors of Summarized Original Work

1983; Baker

1994; Baker

Problem Definition

Many NP-hard graph problems become easier to approximate on planar graphs and their generalizations. (A graph is planar if it can be drawn in the plane (or the sphere) without crossings. For definitions of other related graph classes, see the entry on Bidimensionality (2004; Demaine, Fomin, Hajiaghayi, Thilikos).) For example, a maximum independent set asks to find a maximum subset of vertices in a graph that induce no edges. This problem is inapproximable in general graphs within a factor of n1−ε for any ε > 0 unless NP = ZPP (and inapproximable within \(n^{1/2-\epsilon }\)